Which one of the following is not correct about universal gas constant R?

Options

A. `R=0.0821m^(3)" atm "K^(-1)mol^(-1)`
B. `R=8.314kJK^(-1)mol^(-1)`
C. `R=1.987k.cal^(@)C^(-1)mol^(-1)`
D. All of these

Answer

To determine which statement about the universal gas constant \( R \) is not correct, we will analyze the given options based on the known values and units of \( R \).

### Step 1: Identify the known values of \( R \)
The universal gas constant \( R \) can be expressed in different units:
- In liter atmosphere: \( R = 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1} \)
- In joules: \( R = 8.314 \, \text{J K}^{-1} \text{mol}^{-1} \)
- In calories: \( R = 1.987 \, \text{cal K}^{-1} \text{mol}^{-1} \)

### Step 2: Analyze the options
We need to examine each option provided to determine if any of them incorrectly represent \( R \).

1. **Option 1**: \( R \) is expressed in atmosphere, Kelvin inverse, and mole inverse. This is correct as it matches the unit \( 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1} \).

2. **Option 2**: \( R \) is expressed in joules. This is also correct as it matches \( 8.314 \, \text{J K}^{-1} \text{mol}^{-1} \).

3. **Option 3**: \( R \) is expressed in kilojoules or kilocalories. This is incorrect because the standard values of \( R \) do not include kilojoules or kilocalories directly; they are typically given in joules or calories.

### Step 3: Conclusion
Based on the analysis, the option that is not correct about the universal gas constant \( R \) is the one that refers to kilojoules or kilocalories.

### Final Answer
The statement that is not correct about the universal gas constant \( R \) is the one that refers to it being expressed in kilojoules or kilocalories.

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